# Plotting data in a weird format

I have a lot of data on the following form:

data = {{param1,param2,param3,param4,{{x1,y1},{x2,y2},...,{xn,yn}}},...}


The first variables in each sublist are parameters which were used to generate the data and for each there are only finitely many, i.e. param1 is in the set {1,2,3,4} and param2 in the set {0,0.25,0.5}. Each possible param sequence is guaranteed to appear exactly once.

Now I would like to create all plots where a couple (or arbitrarily many) of the parameters are fixed but the other ones can vary. For example, one plot would have param1 to be 1 and param2 to be 0.5 then the corresponding Plot would vary param3 and param4 over their possible values.

Is it possible to do this with relatively little code?

Edit: Here is some data if you want to practice:

data = {{0.05,0.25,2,0.05,{{10,1.81095078464},{20,4.67233914533},{30,7.08803699724},{40,12.2604831338},{50,4.4765112617},{60,30.4472408052},{70,13.9643317682},{80,41.2579927871},{90,11.960557746}}}
,{0.05,0.25,2,0.1,{{10,2.43799671091},{20,6.61987906477},{30,0.0668059190229},{40,2.7061070004},{50,18.8102895497},{60,24.4730064793},{70,20.2747124961},{80,74.8539284102},{90,47.2172814344}}}
,{0.05,0.25,2,0.15,{{10,2.67074811192},{20,15.9521439491},{30,3.54972604159},{40,13.1682228406},{50,23.6066621641},{60,12.4390170784},{70,46.0070233365},{80,38.0116375085},{90,12.0705695205}}}
,{0.05,0.25,3,0.05,{{10,3.1269953325},{20,15.6996942029},{30,24.1145670018},{40,36.0334138554},{50,41.1150906489},{60,31.4063841784},{70,34.4001494185},{80,9.52491909762},{90,15.5320891272}}}
,{0.05,0.25,3,0.1,{{10,9.6198670177},{20,1.68271939508},{30,14.4069805301},{40,32.0147092546},{50,26.7042711284},{60,47.7967863197},{70,46.7059123396},{80,57.809041849},{90,84.4256784391}}}
,{0.05,0.25,3,0.15,{{10,3.62785141167},{20,7.48741493046},{30,2.08245578621},{40,36.2518798094},{50,20.0541864045},{60,38.5706584591},{70,42.2491352509},{80,33.8688792853},{90,12.5218627351}}}
,{0.05,0.25,4,0.05,{{10,6.113253503},{20,3.34466308592},{30,22.8994502487},{40,27.8256812834},{50,42.3128480576},{60,11.8814975842},{70,23.6489403538},{80,67.2170848449},{90,64.7381753617}}}
,{0.05,0.25,4,0.1,{{10,6.63675406908},{20,14.2655858882},{30,2.16789822064},{40,34.6305949789},{50,31.7812530609},{60,45.0207978304},{70,29.9999048737},{80,66.9741618718},{90,55.0452401763}}}
,{0.05,0.25,4,0.15,{{10,6.90255549999},{20,3.9885321713},{30,26.7487549741},{40,17.9087260172},{50,15.897872199},{60,9.29221539717},{70,59.9905412021},{80,51.2029208226},{90,43.2240798207}}}
,{0.05,0.25,5,0.05,{{10,2.03521621274},{20,10.6802820552},{30,22.7668370169},{40,17.4842532703},{50,33.8885022742},{60,53.1974918374},{70,60.2751976503},{80,40.7192672242},{90,83.5475720189}}}
,{0.05,0.25,5,0.1,{{10,7.67431501913},{20,1.95859099835},{30,23.3519464193},{40,13.8993657827},{50,31.6415181272},{60,23.1976359038},{70,35.0005300883},{80,17.0312839157},{90,57.0400103646}}}
,{0.05,0.25,5,0.15,{{10,5.06555796312},{20,10.9204321376},{30,21.8069692381},{40,19.5772020736},{50,11.3270822542},{60,4.81298507075},{70,59.7538646808},{80,66.1476668838},{90,73.1291546231}}}
,{0.05,0.5,2,0.05,{{10,4.64402575054},{20,11.0700265682},{30,13.5807209068},{40,17.4950974568},{50,10.358793839},{60,15.8021221186},{70,63.1214522278},{80,57.8308798847},{90,22.5414408889}}}
,{0.05,0.5,2,0.1,{{10,4.38798903726},{20,3.70039642682},{30,25.1663321348},{40,5.08534158813},{50,30.2269860186},{60,12.9107480373},{70,10.2495871724},{80,41.7860842547},{90,21.3519476486}}}
,{0.05,0.5,2,0.15,{{10,6.77220056497},{20,7.38600235623},{30,11.5745943742},{40,30.5829816576},{50,38.589061723},{60,57.6488293351},{70,1.26057229892},{80,5.9267804496},{90,82.6704015928}}}
,{0.05,0.5,3,0.05,{{10,3.32034254713},{20,10.971486433},{30,0.363147390123},{40,37.65329461},{50,15.949633583},{60,21.8418741365},{70,28.3562497933},{80,71.7087071989},{90,79.5554695131}}}
,{0.05,0.5,3,0.1,{{10,1.58954955321},{20,3.76237825847},{30,17.5550842398},{40,29.2109934963},{50,6.49252024706},{60,51.8137399056},{70,41.9546186462},{80,24.1401496171},{90,84.1640682329}}}
,{0.05,0.5,3,0.15,{{10,9.01150441341},{20,10.9523361655},{30,20.6533901253},{40,24.3713540557},{50,8.20484429104},{60,1.16388638136},{70,2.7717770797},{80,36.0311528516},{90,79.6148650441}}}
,{0.05,0.5,4,0.05,{{10,2.64807693809},{20,17.4186809674},{30,11.0988927114},{40,12.9430380703},{50,20.1267053993},{60,56.2647281546},{70,69.2811052248},{80,27.6645633652},{90,85.1136096421}}}
,{0.05,0.5,4,0.1,{{10,6.02663873848},{20,2.63294032126},{30,7.74879650203},{40,8.27484945215},{50,5.95510226084},{60,52.6154234102},{70,12.511545849},{80,78.8192910206},{90,12.3488606088}}}
,{0.05,0.5,4,0.15,{{10,8.25216926779},{20,7.60388967899},{30,1.0533107346},{40,2.21081169594},{50,35.7020132845},{60,57.911449844},{70,17.5890809513},{80,15.1115721942},{90,1.02639298919}}}
,{0.05,0.5,5,0.05,{{10,8.49277943149},{20,2.51406868421},{30,11.4011785147},{40,39.4308578521},{50,39.8307541943},{60,35.5969342248},{70,62.2928703256},{80,71.5575481117},{90,61.6565219289}}}
,{0.05,0.5,5,0.1,{{10,3.425448449},{20,10.3597097543},{30,6.19100953018},{40,10.4540143146},{50,23.2857082412},{60,17.3599512427},{70,28.7492345283},{80,35.9268076613},{90,23.5710386153}}}
,{0.05,0.5,5,0.15,{{10,2.87691906629},{20,15.5942388106},{30,27.7675182329},{40,26.9156263637},{50,30.0860121249},{60,46.5691600184},{70,59.5923947398},{80,13.3664590053},{90,46.9926862072}}}
,{0.05,0.75,2,0.05,{{10,2.33118591118},{20,0.171302391205},{30,3.8162801126},{40,38.1028271195},{50,15.9557228127},{60,10.9717594589},{70,50.4761540499},{80,34.2194752184},{90,57.3320890909}}}
,{0.05,0.75,2,0.1,{{10,9.21187915809},{20,15.931228085},{30,13.2347014451},{40,2.09075850626},{50,35.9255672695},{60,33.953217097},{70,16.9449485001},{80,3.7436362842},{90,35.5772239774}}}
,{0.05,0.75,2,0.15,{{10,0.791065400588},{20,14.0143142872},{30,3.37600328092},{40,22.3812487398},{50,21.1693240081},{60,19.7087594303},{70,68.1887031769},{80,38.0093505188},{90,37.7895850656}}}
,{0.05,0.75,3,0.05,{{10,9.31810727853},{20,9.76215342921},{30,7.76683101607},{40,35.3384426319},{50,44.4717515812},{60,53.5710585193},{70,45.4840193583},{80,59.5407627578},{90,60.4710222303}}}
,{0.05,0.75,3,0.1,{{10,2.53659798611},{20,4.70704669175},{30,18.2959346871},{40,35.9224308806},{50,36.5480039338},{60,43.4640708957},{70,7.24722453278},{80,40.943093786},{90,81.9694316569}}}
,{0.05,0.75,3,0.15,{{10,0.100105878083},{20,15.6660867132},{30,23.5308070875},{40,8.19490108256},{50,6.02445100435},{60,28.6216840496},{70,69.2893512352},{80,3.7744156909},{90,80.9475721672}}}
,{0.05,0.75,4,0.05,{{10,8.0933835982},{20,18.9656256251},{30,18.4700662413},{40,1.67540094072},{50,12.411938782},{60,1.63616227618},{70,12.593678348},{80,70.6808044911},{90,53.8566296064}}}
,{0.05,0.75,4,0.1,{{10,3.19835596466},{20,19.0476174241},{30,1.58525644896},{40,4.57246061776},{50,41.0673261923},{60,30.72857255},{70,11.9372932092},{80,76.8378358811},{90,23.608111421}}}
,{0.05,0.75,4,0.15,{{10,6.6446636599},{20,0.295275665136},{30,11.6826665238},{40,16.6603278505},{50,42.0122936272},{60,51.8210661871},{70,37.1211762546},{80,28.8305779696},{90,15.4410237106}}}
,{0.05,0.75,5,0.05,{{10,4.44734165144},{20,6.66893577711},{30,3.55054836325},{40,9.4767095531},{50,25.7843768065},{60,24.2743878743},{70,34.2370917884},{80,34.9507738144},{90,83.5111434619}}}
,{0.05,0.75,5,0.1,{{10,7.84586864359},{20,12.0472863816},{30,27.395358028},{40,7.26350803368},{50,2.6064473865},{60,51.377539089},{70,31.276369458},{80,59.1499919813},{90,31.8353206328}}}
,{0.05,0.75,5,0.15,{{10,2.20956347811},{20,11.078484084},{30,5.07233531175},{40,38.1356170453},{50,29.6534616181},{60,6.38250659035},{70,62.4726098813},{80,33.6021622135},{90,29.8045456453}}}
,{0.05,1,2,0.05,{{10,6.77714943938},{20,5.657718189},{30,19.0493303978},{40,39.636743496},{50,34.5096155839},{60,13.9300761353},{70,45.9834142675},{80,4.64884310707},{90,59.6849298315}}}
,{0.05,1,2,0.1,{{10,3.86505813154},{20,10.0886018939},{30,6.65846439181},{40,26.1224551281},{50,30.9014736954},{60,11.4155036781},{70,33.0291680043},{80,74.6509229773},{90,36.9492872204}}}
,{0.05,1,2,0.15,{{10,1.99654946557},{20,16.2049557761},{30,26.1363569323},{40,38.7372287427},{50,40.2025346552},{60,39.8858065844},{70,10.3023904166},{80,41.8886418279},{90,70.9094529273}}}
,{0.05,1,3,0.05,{{10,2.34518030674},{20,12.2556329339},{30,3.05566675163},{40,26.8300477228},{50,30.6367983486},{60,19.4331000773},{70,62.9975381973},{80,73.4322628917},{90,39.1957337766}}}
,{0.05,1,3,0.1,{{10,7.68796282248},{20,15.9096854918},{30,4.54025818601},{40,7.45388052723},{50,12.457354139},{60,24.3015045943},{70,50.2688106134},{80,36.1148253991},{90,67.9233729094}}}
,{0.05,1,3,0.15,{{10,4.65218387794},{20,16.8386602868},{30,25.5930142898},{40,7.82172541215},{50,1.29242214896},{60,21.5544155961},{70,31.7440802727},{80,19.2507862987},{90,4.07000801216}}}
,{0.05,1,4,0.05,{{10,0.69101208094},{20,9.34880796351},{30,7.17856203574},{40,30.112388804},{50,40.8619565867},{60,9.43604345999},{70,69.6804647491},{80,32.8742327742},{90,36.8468278409}}}
,{0.05,1,4,0.1,{{10,7.52710101478},{20,10.4920352043},{30,15.4111870748},{40,35.6243877241},{50,3.94992669146},{60,49.8266439283},{70,69.5140218785},{80,70.5337864009},{90,85.3876987564}}}
,{0.05,1,4,0.15,{{10,3.62234353787},{20,14.2397062922},{30,25.1356228484},{40,37.8715362786},{50,23.6113234196},{60,48.1540335361},{70,10.2338938212},{80,34.8127725764},{90,54.6251642429}}}
,{0.05,1,5,0.05,{{10,3.42309751666},{20,12.8828592654},{30,5.04947596019},{40,37.9218907866},{50,33.1506882433},{60,37.6953472861},{70,5.73178257281},{80,7.03749358685},{90,79.2393944507}}}
,{0.05,1,5,0.1,{{10,3.77053553619},{20,7.42357221292},{30,19.8494673301},{40,27.7478936358},{50,46.6825595981},{60,12.1764819866},{70,57.2046605066},{80,65.2407822409},{90,33.7164233635}}}
,{0.05,1,5,0.15,{{10,6.49191956291},{20,5.32890967287},{30,13.1398913983},{40,25.8084558834},{50,44.0679908978},{60,16.0657787413},{70,65.846463301},{80,5.709476188},{90,50.5077277368}}}
,{0.1,0.25,2,0.05,{{10,8.1805131568},{20,13.3839416884},{30,5.35535429554},{40,31.1637561463},{50,29.2251514633},{60,56.7644536173},{70,28.6419959787},{80,77.7369839641},{90,64.1029710405}}}
,{0.1,0.25,2,0.1,{{10,4.00140666299},{20,10.8863043703},{30,2.81582596423},{40,27.4965991947},{50,25.0337108129},{60,12.1412568651},{70,21.2241844654},{80,55.4861523882},{90,84.2383928999}}}
,{0.1,0.25,2,0.15,{{10,6.53764557883},{20,3.1053903961},{30,11.515699156},{40,25.6597655992},{50,44.0127890186},{60,46.0691492929},{70,56.2843023454},{80,43.1056203069},{90,28.4124452184}}}
,{0.1,0.25,3,0.05,{{10,0.721470639814},{20,14.5078204964},{30,17.2573095333},{40,36.1034897775},{50,40.4045204395},{60,55.1468706076},{70,56.6263585656},{80,51.9798227207},{90,14.6412003494}}}
,{0.1,0.25,3,0.1,{{10,2.87370884284},{20,4.56253572796},{30,14.6945541145},{40,13.9546874469},{50,7.4818924749},{60,16.5381563607},{70,20.3566470069},{80,38.6153112546},{90,48.0178060833}}}
,{0.1,0.25,3,0.15,{{10,2.83875203825},{20,15.0609608907},{30,17.5240166232},{40,22.4293300139},{50,21.6102852167},{60,9.15004256886},{70,45.6354523511},{80,69.5680089543},{90,5.71728103804}}}
,{0.1,0.25,4,0.05,{{10,4.46646009433},{20,5.7320048815},{30,11.4016738341},{40,8.83523265091},{50,16.4847370272},{60,36.8009395286},{70,24.5999040271},{80,14.1650741968},{90,8.02876977497}}}
,{0.1,0.25,4,0.1,{{10,0.488156430383},{20,9.73307404131},{30,0.597418004153},{40,23.0552672427},{50,16.2087532724},{60,34.43009287},{70,27.3554342695},{80,70.311017112},{90,28.0188921989}}}
,{0.1,0.25,4,0.15,{{10,5.3461674224},{20,2.91528771185},{30,18.9550685617},{40,17.5601781976},{50,35.342927073},{60,3.18860635682},{70,52.5782031356},{80,11.2419622939},{90,79.0487883136}}}
,{0.1,0.25,5,0.05,{{10,3.24319494011},{20,9.20282886188},{30,15.2186717481},{40,23.3891524884},{50,36.1335727272},{60,38.6728479249},{70,41.9240629723},{80,22.7397645521},{90,9.30747274433}}}
,{0.1,0.25,5,0.1,{{10,7.59497995474},{20,0.405926294602},{30,11.8418092773},{40,34.5152511797},{50,33.1815145209},{60,18.2661886311},{70,25.4418955824},{80,31.9778916064},{90,73.9786748628}}}
,{0.1,0.25,5,0.15,{{10,6.12961088543},{20,19.9331364341},{30,18.2545077545},{40,15.1198651774},{50,26.0912471551},{60,35.1203226514},{70,12.2285551291},{80,72.1932144614},{90,53.0386701391}}}
,{0.1,0.5,2,0.05,{{10,7.59488953517},{20,11.2978335861},{30,22.5064570351},{40,2.35265743589},{50,0.908253825134},{60,56.5655545397},{70,27.0860153547},{80,78.0129191571},{90,49.7715169565}}}
,{0.1,0.5,2,0.1,{{10,1.43860542157},{20,16.0605769084},{30,4.63441645706},{40,21.4207950368},{50,7.68008769367},{60,34.8078464101},{70,26.8410066037},{80,31.5708973783},{90,32.8848746975}}}
,{0.1,0.5,2,0.15,{{10,8.39514333251},{20,10.0341828507},{30,9.38010187697},{40,34.4526749456},{50,5.80913020794},{60,51.8092369073},{70,49.3295337536},{80,55.6237692935},{90,61.8200747267}}}
,{0.1,0.5,3,0.05,{{10,9.38641922534},{20,17.9040760206},{30,0.25707206566},{40,34.093764649},{50,34.5677933731},{60,19.2397646578},{70,33.2670768537},{80,47.890923252},{90,34.3797445311}}}
,{0.1,0.5,3,0.1,{{10,4.00465844105},{20,15.5385282854},{30,18.6173588469},{40,22.6123989951},{50,1.62301944438},{60,18.1239726264},{70,17.3044858704},{80,22.0666086744},{90,11.5168991949}}}
,{0.1,0.5,3,0.15,{{10,2.56845586386},{20,13.0816651606},{30,17.8228500021},{40,37.6102328305},{50,8.51102447018},{60,7.89016813299},{70,41.0452165717},{80,58.5787413693},{90,18.2308463676}}}
,{0.1,0.5,4,0.05,{{10,2.49727084491},{20,3.56416194578},{30,6.27724685884},{40,6.72849195117},{50,43.2802722534},{60,26.4631951187},{70,10.1557053085},{80,11.5753957119},{90,59.7621806738}}}
,{0.1,0.5,4,0.1,{{10,7.60259722645},{20,6.0118465907},{30,28.0628724627},{40,31.3206046138},{50,21.9790486839},{60,16.6828749185},{70,58.8901143246},{80,64.3715017101},{90,6.40250308925}}}
,{0.1,0.5,4,0.15,{{10,9.37837560535},{20,9.30356878331},{30,5.68459387165},{40,28.3961060974},{50,29.9119490477},{60,33.244421553},{70,43.4853149932},{80,62.8169391547},{90,35.0986227335}}}
,{0.1,0.5,5,0.05,{{10,5.46777855196},{20,0.307003624332},{30,5.57189679082},{40,8.58812353128},{50,12.2046576077},{60,25.5712910446},{70,69.7711454398},{80,60.98627112},{90,8.24922668557}}}
,{0.1,0.5,5,0.1,{{10,0.621904144918},{20,4.84235895254},{30,3.81862601241},{40,21.0939034156},{50,38.4562570489},{60,57.3622032991},{70,34.6407205654},{80,8.55277344038},{90,0.777217632246}}}
,{0.1,0.5,5,0.15,{{10,5.7173069971},{20,4.10396300275},{30,24.0751334673},{40,6.41106554954},{50,45.6411938905},{60,0.464834918316},{70,65.728589585},{80,32.7945564693},{90,24.0931788427}}}
,{0.1,0.75,2,0.05,{{10,8.9647599673},{20,13.8216677501},{30,20.6509238656},{40,20.365515982},{50,37.3223482332},{60,24.2570338722},{70,62.0867170638},{80,59.4777900977},{90,72.215984611}}}
,{0.1,0.75,2,0.1,{{10,8.42005651213},{20,17.4999589292},{30,3.18182290422},{40,31.8665894313},{50,48.8812894167},{60,10.6751908611},{70,46.9148403878},{80,0.417086397777},{90,89.4324954751}}}
,{0.1,0.75,2,0.15,{{10,6.44725231886},{20,10.9257419595},{30,21.3480009383},{40,11.2193148168},{50,36.2819546524},{60,25.1980712824},{70,56.4458146677},{80,10.108865306},{90,26.3041268147}}}
,{0.1,0.75,3,0.05,{{10,4.76687201456},{20,2.78989303629},{30,3.67872578585},{40,24.1374000229},{50,3.13458262944},{60,22.2339463736},{70,17.0706266227},{80,0.46493078169},{90,65.959591258}}}
,{0.1,0.75,3,0.1,{{10,6.50453054541},{20,7.66629452689},{30,2.18985081258},{40,21.4462060735},{50,16.3647659138},{60,38.586050839},{70,11.6351479006},{80,0.84607270655},{90,7.05753337902}}}
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-
What is it precisely you want to plot? The $(x,y)$ pairs as a line? Or something computed from them? If you just want to plot $(x,y)$ as a line, then are you aiming to create as many plots as there are freely variable param values or do you need all lines on a single plot? Or perhaps you're looking for something computed from that line (e.g. its slope) as a function of the free params? –  Szabolcs Mar 10 at 15:47
Yes precisely, the (x,y) pairs as a line. I want all of the lines on a single plot (but for each 2-subset I want a separate plot). Thanks! –  Haffi112 Mar 10 at 15:52
Please add some actual data to work with. –  Yves Klett Mar 10 at 16:06
Ok, will do. Just a moment! –  Haffi112 Mar 10 at 16:08

Edit Keep in mind points that Mr. Wizard has pointed in comments below that answer.

Big and only advantage of this method is compactness. So in this context if I had to make more reliable solution (longer) I'd rather use database approach.

You can use Cases. For solid solution when your data is huge and static I'd use some kind database approach probably, but have not got experience so that's all to say:)

This however, is quite short and can benefit from pattern matching possibilities:

ListLinePlot @ Cases[data, {0.05, 0.25, _, _, x_} :> x]


ListLinePlot @ Cases[data, {0.05 | 0.15, 0.25, 2, 0.1, x_} :> x]


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This is perfect, short and functional :) Thanks a lot! –  Haffi112 Mar 11 at 8:36
@Haffi112 It is inadvisable to use verbatim inexact numbers in patterns as done above. Instead you should use e.g. n_ /; n == 0.05. Please see (5149) and (15907) for an explanation. –  Mr.Wizard Mar 11 at 9:19
@Mr.Wizard I wouldn't call it inadvisable. Just be aware of the difference between 2 and 2. and how MatchQ works. But good point. –  Kuba Mar 11 at 9:23
Kuba, respectfully, I don't think that's enough. The point is that you often cannot be certain that an inexact number with have the same internal representation, therefore even if all your numbers are inexact the pattern you gave may fail to match. One could of course Rationalize all values but that brings its own issues. Restating my position: your use the pattern {0.05, 0.25, _, _, x_} is prone to subtle and frustrating bugs. –  Mr.Wizard Mar 11 at 12:43
@Mr.Wizard I think my edit is fair now :) –  Kuba Mar 12 at 20:14

Building from the answer to the following question How can a big table be treated as a database

 (*Include your data above *)
titles = {"paramA", "paramB", "paramC", "ParamD", "Values"};
PrependTo[data, titles];

SetAttributes[queryCriteria, HoldAll]
queryCriteria[theTable_, query_] :=
Function[{entry},
Unevaluated[query] /. (Rule @@@ Transpose[{theTable[[1]], entry}]),
HoldAll]

ListPlot[Select[data,
queryCriteria[data, "paramA" == 0.15 && "paramB" == 1]][[All, 5]],
Joined -> True]

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